How do I re-size (scale) a model with the textures applied at the same time?
Textures follow UVs which in turn follow your model's vertices wherever they go (assuming your model has standard UV mapping as opposed to projected UVs), so scaling the model will have no effect on your texture resolution or placement. 

Best practice generally is to have the pivot points - aka origins - of both mesh and armature at centre - 0,0,0 - although it's not essential, just neater.

Assuming you have that, scale your entire mesh in edit mode, ideally from cursor and cursor placed at centre until it fits your armature-  you may need to move it in Y to align with your bones.

Alternately scale all your armature bones up in edit mode, again from centre, although that will affect any animation already on it, so scaling mesh is a better option.

Either way you may need to tweak the position of the bones in edit mode to match you mesh if there are small mismatches. Animation is likely to be the same for small changes as the position of bones in edit mode are considered 0,0,0 in pose mode regardless of world position.

Hope I understood the question correctly .....